When x³ + 2x² - kx + 4 is divided by x - 2, the remainder is k. Find the value of constant k.

x - 2 = 0 ⇒ x = 2.

Given, when x³ + 2x² - kx + 4 is divided by x - 2, the remainder is k.

∴ On substituting x = 2 in x³ + 2x² - kx + 4, remainder = k.

⇒ (2)³ + 2(2)² - k(2) + 4 = k

⇒ 8 + 8 - 2k + 4 = k

⇒ 20 - 2k = k

⇒ 3k = 20

⇒ k = $\dfrac{20}{3} = 6\dfrac{2}{3}.$

Hence, k = $6\dfrac{2}{3}.$